Course Learning Goals

determine a basis for a vector space and the dimension of a vector space;

determine coordinates for a vector relative to a given basis;

perform dot product and apply to defining norm and orthogonality;

recognize a linear mapping;

determine domain, null space, and range for a given linear mapping and relate the dimensions of these three vector spaces;

find a matrix for a linear mapping;

perform matrix products (composition of mappings);

find an inverse of a nonsingular matrix (inverse of a mapping);

apply matrix algebra to Leontief model, population model;

evaluate determinant and relate to theory;

recognize similar matrices;

determine eigenvalues and eigenvectors;

determine diganonability; and

apply theory of eigenvalues to Markov model.

Planned Sequence of Topics and/or Learning Activities

Systems of Equations

Solutions using matrices

Row reduction

Existence and uniqueness of solutions

Set of solutions as an example of a vector space

Matrices

Matrix equations

Vector Spaces

Definitions

Examples: Rn, C[0,1]

Subspaces

Independence and spanning

Bases and coordinates

Geometric Examples

R2 and R3

Dot product

Norm

Orthogonality

Linear Mappings

Homomorphisms, isomorphisms

Null space of mapping

Linear mappings

Composition of mappings

Product of matrices

Inverse of a mapping

Inverse of a matrix

Algebra of matrices

Determinants

Leontief models

Similar matrices

Eigen vectors and values

Diagonability

Invariant subspaces

Markov chains

Quadratic forms - optional

Assessment Methods for Course Learning Goals

The student will apply mathematical concepts and principles to identify and solve problems presented through informal assessment, such as oral communication among students and between teacher and students. Formal assessment will consist of open-ended questions reflecting theoretical and applied situations.

Reference, Resource, or Learning Materials to be used by Student:

Departmentally-selected textbook. Details provided by the instructor of each course section. See course syllabus.